Answer to Question #220045 in Mechanics | Relativity for Alex

Question

a - A child of mass 30 kg travels in a lift. Calculate the force exerted on the child by

the floor of the lift when the lift moves (i) downward with an acceleration of 1.0 ms^-2 , (ii) upward with an acceleration of 1.0 ms^-2 What is the weight of the

child when the lift falls freely? Take g = 10 ms^-2

b- A satellite of mass 200 kg is displaced by a distance of 2R_efrom a point on the

Earth’s surface, where R_e is the radius of the Earth. Calculate the work done on

the satellite by the force of gravitation. Take the values of the constants in your

calculation from the astrophysical data given in the course.

Answer 1

(a)

(i)

$$N-mg=-ma,$$ $$N=m(g-a)=30\ kg\cdot(10\ \dfrac{m}{s^2}-1\ \dfrac{m}{s^2})=270\ N.$$

(ii)

$$N-mg=ma,$$ $$N=m(g+a)=30\ kg\cdot(10\ \dfrac{m}{s^2}+1\ \dfrac{m}{s^2})=330\ N.$$

(iii) In free fall the acceleration will be directed downward and we get: 

$$N=m(g-a)=m(g-g)=0\ N.$$

(b) By the definition of the work done, we have:

$$W_g=F_gd=mgh=mg2R_e,$$ $$W_g=200\ kg\cdot9.8\ \dfrac{m}{s^2}\cdot2\cdot6.371\cdot10^6\ m=2.5\cdot10^{10}\ J.$$